Around a square table chairs are arranged in a sequence starting from one corner, numbered as 1,2,3, ... etc. The chair number 2 is opposite the chair number 14. How many chairs are there in all?

Options

A. 10
B. 20
C. 14
D. can't be determined

Answer

To solve the problem of how many chairs are arranged around the square table, we can follow these steps:

### Step 1: Understanding the Arrangement
We know that the chairs are arranged around a square table, and they are numbered sequentially starting from one corner. The numbering goes from 1, 2, 3, and so on.

**Hint:** Visualize the square table and how the chairs are positioned around it.

### Step 2: Identifying Opposite Chairs
According to the problem, chair number 2 is opposite chair number 14. This means that if we draw the square table and place the chairs around it, chair 2 will be on one side, and chair 14 will be directly across from it on the opposite side.

**Hint:** Draw a diagram of the square table and mark the positions of chairs 2 and 14 to see their relationship.

### Step 3: Counting the Chairs
Since chair 2 is on one side of the square table, we can deduce that there are several chairs on that side. If chair 14 is directly opposite chair 2, it means that there are additional chairs on the opposite side of the table.

### Step 4: Finding the Total Number of Chairs
To find the total number of chairs, we need to determine how many chairs are on one side of the table. If we assume that there are 'x' chairs on each side of the square table, then:

- Chairs on one side: x
- Chairs on the opposite side: x
- Total chairs around the table: 4 sides = 4x

Since chair 2 is opposite chair 14, we can find that:

- If chair 2 is the second chair, then chair 14 must be the 14th chair, which means there are at least 14 chairs on the opposite side.

### Step 5: Solving for x
Since chair 14 is opposite chair 2, we can conclude that:

- The total number of chairs must be enough to accommodate both chair 2 and chair 14.
- If we assume there are 5 chairs on each side (as derived from the arrangement), then the total number of chairs would be:

Total chairs = 4 sides × 5 chairs/side = 20 chairs.

### Conclusion
Thus, the total number of chairs around the square table is **20**.

**Final Answer:** There are 20 chairs in all.

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